reserve A for set,
  C for non empty set,
  B for Subset of A,
  x for Element of A,
  f,g for Function of A,C;
reserve B for Element of Fin A;

theorem Th9:
  dom (g|B) = B
proof
  reconsider C = B as Subset of A by FINSUB_1:16;
  dom (g|C) = C by Th1;
  hence thesis;
end;
